170. On the assumption that particulars are interpreted as implying while universals are not interpreted as implying the existence of their subjects in the universe of discourse, examine (stating your reasons) the validity of the following inferences; All S is P and Some R is not S therefore, Some not-S is not P ; All S is P and Some R is not P, therefore, Some not-S is 248 not P ; All S is P and Some R is S, it is, therefore, false that No P is S ; All S is P and Some R is P, it is, therefore, false that No P is S. [K.]
171. Discuss the formal validity of the following arguments, (i) on the supposition that all categorical propositions are to be interpreted as implying the existence of their subjects in the universe of discourse, (ii) on the supposition that no categorical propositions are to be so interpreted:
(a) All P is Q, therefore, All AP is AQ ;
(b) All AP is AQ, therefore, Some P is Q. [K.]
172. Work out the doctrine of Opposition and the doctrine of Immediate Inferences on the hypothesis that universals are to be interpreted as implying, while particulars are not to be interpreted as implying, the existence of their subjects in the universe of discourse. [K.]
CHAPTER IX.
CONDITIONAL AND HYPOTHETICAL PROPOSITIONS.
173. The distinction between Conditional Propositions and Hypothetical Propositions[268]—Propositions commonly written in the form If A is B, C is D belong to two very different types. For they may be the expression either of simple judgments or of compound judgments (as distinguished in section [55]).
[268] For the distinction indicated in the present section I was in the first instance indebted to an essay, written in 1884, by Mr W. E. Johnson. This essay has not been published in its original form; but the substance of it has been included in some papers on The Logical Calculus by Mr Johnson which appeared in Mind in 1892.
In the first place, A being B and C being D may be two events or two combinations of properties, concerning which it is affirmed that whenever or wherever the first occurs the second will occur also. For example, If an import duty is a source of revenue, it does not afford protection ; If a child is spoilt, his parents suffer ; If a straight line falling upon two other straight lines makes the alternate angles equal to one another, the two straight lines are parallel to one another ; If a lighted match is applied to gunpowder, there will be an explosion ; Where the carcase is, there shall the eagles be gathered together. What is affirmed in all such cases as these is a connexion between phenomena; it may be either a co-inherence of attributes in a common subject, or a relation in time or space between certain occurrences. Propositions belonging to this type may be called distinctively conditional.
But again, A is B and C is D may be two propositions of independent import, the relation between which cannot be 250 directly resolved into any time or space relation or into an affirmation of the co-inherence of attributes in a common subject. In other words, a relation may be affirmed between the truth of two judgments as holding good once and for all without distinction of place or time or circumstance. For example, If it be a sin to covet honour, I am the most offending soul alive ; If patience is a virtue, there are painful virtues ; If there is a righteous God, the wicked will not escape their just punishment ; If virtue is involuntary, so is vice ; If the earth is immoveable, the sun moves round the earth. Propositions belonging to this type may be called hypothetical as distinguished from conditional, or they may be spoken of still more distinctively as true hypotheticals or pure hypotheticals.[269]